Energy balance and the Malthusian parameter, m, of grazing small rodents : A graphic model

A graphic model based on cost and gain functions is developed for predicting the relative magnitude of the Malthusian parameter, m, for different phenotypes. The analysis is mainly restricted to grazing small rodents. The cost function is derived by depicting the probability of death due to predation, parasitism etc. as a function of time spent outside the nest. The gain function is derived by comparing the energy obtained by digestion, with energy used (or needed) for maintenance metabolism, both when outside and inside the nest.The model is applied for predicting the relative magnitude of the Malthusian parameter of small versus large phenotypes of grazing rodents. Of these, the smaller phenotypes are concluded to have the larger Malthusian parameter. This may not hold true for hunters (granivores and predators). These conclusions are used for reinterpreting the often observed geographical size trend in warm-blooded vertebrates (Bergmann's rule).The model is further applied to the determination of the relative magnitude of the Malthusian parameter for aggresive and docile strategies hypothesized in Chitty's theory for fluctuating populations. Of these, the aggressive strategy is concluded to have the lowest Malthusian parameter. Although not verifying Chitty's theory, these results support the earlier hypothesis that the aggressive strategy may under certain situations have lower survival. Based on the present model, nothing can be said about whether or not a polymorphic population as hypothesized by Chitty will exhibit oscillations.